Read e-book online Euler's Gem: The Polyhedron Formula and the Birth of PDF

By David S. Richeson

Leonhard Euler's polyhedron formulation describes the constitution of many objects--from football balls and gem stones to Buckminster Fuller's structures and sizeable all-carbon molecules. but Euler's formulation is so easy it may be defined to a toddler. Euler's Gem tells the illuminating tale of this crucial mathematical idea.

From old Greek geometry to trendy state of the art examine, Euler's Gem celebrates the invention of Euler's loved polyhedron formulation and its far-reaching influence on topology, the research of shapes. In 1750, Euler saw that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks ignored the formulation solely; how Descartes nearly came upon it yet fell brief; how nineteenth-century mathematicians widened the formula's scope in ways in which Euler by no means predicted by way of adapting it to be used with doughnut shapes, soft surfaces, and better dimensional shapes; and the way twentieth-century mathematicians chanced on that each form has its personal Euler's formulation. utilizing significant examples and various illustrations, Richeson provides the formula's many stylish and unforeseen functions, akin to exhibiting why there's consistently a few windless spot in the world, tips on how to degree the acreage of a tree farm by means of counting timber, and the way many crayons are had to colour any map.

packed with a who is who of extraordinary mathematicians who wondered, subtle, and contributed to a amazing theorem's improvement, Euler's Gem will fascinate each arithmetic enthusiast.

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Euler's Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson


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